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An inertial ADMM for a class of nonconvex composite optimization with nonlinear coupling constraints

Author

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  • Le Thi Khanh Hien

    (Huawei Belgium Research Center)

  • Dimitri Papadimitriou

    (Huawei Belgium Research Center)

Abstract

In this paper, we propose an inertial alternating direction method of multipliers for solving a class of non-convex multi-block optimization problems with nonlinear coupling constraints. Distinctive features of our proposed method, when compared with other alternating direction methods of multipliers for solving non-convex problems with nonlinear coupling constraints, include: (i) we apply the inertial technique to the update of primal variables and (ii) we apply a non-standard update rule for the multiplier by scaling the multiplier by a factor before moving along the ascent direction where a relaxation parameter is allowed. Subsequential convergence and global convergence are presented for the proposed algorithm.

Suggested Citation

  • Le Thi Khanh Hien & Dimitri Papadimitriou, 2024. "An inertial ADMM for a class of nonconvex composite optimization with nonlinear coupling constraints," Journal of Global Optimization, Springer, vol. 89(4), pages 927-948, August.
    • Handle: RePEc:spr:jglopt:v:89:y:2024:i:4:d:10.1007_s10898-024-01382-4
    DOI: 10.1007/s10898-024-01382-4
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    References listed on IDEAS

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    1. Jérôme Bolte & Shoham Sabach & Marc Teboulle, 2018. "Nonconvex Lagrangian-Based Optimization: Monitoring Schemes and Global Convergence," Mathematics of Operations Research, INFORMS, vol. 43(4), pages 1210-1232, November.
    2. Le Thi Khanh Hien & Duy Nhat Phan & Nicolas Gillis, 2022. "Inertial alternating direction method of multipliers for non-convex non-smooth optimization," Computational Optimization and Applications, Springer, vol. 83(1), pages 247-285, September.
    3. repec:dau:papers:123456789/4688 is not listed on IDEAS
    4. P. Tseng & S. Yun, 2009. "Block-Coordinate Gradient Descent Method for Linearly Constrained Nonsmooth Separable Optimization," Journal of Optimization Theory and Applications, Springer, vol. 140(3), pages 513-535, March.
    5. Radu Ioan Bot & Dang-Khoa Nguyen, 2020. "The Proximal Alternating Direction Method of Multipliers in the Nonconvex Setting: Convergence Analysis and Rates," Mathematics of Operations Research, INFORMS, vol. 45(2), pages 682-712, May.
    6. Eyal Cohen & Nadav Hallak & Marc Teboulle, 2022. "A Dynamic Alternating Direction of Multipliers for Nonconvex Minimization with Nonlinear Functional Equality Constraints," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 324-353, June.
    7. Maryam Yashtini, 2022. "Convergence and rate analysis of a proximal linearized ADMM for nonconvex nonsmooth optimization," Journal of Global Optimization, Springer, vol. 84(4), pages 913-939, December.
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